How about t in your code expressions ?

You can ask a question in the field at Promt.
Still a bit user-unfriendly for input, because you can't jump to a new line?
Not using the latest version of Chat Gpt yet?
Note: ChatGPT can use uploaded pics with maple code,handy. 

with(NaturalLanguage);
GenerateDocument[interactive]();

The wolf best position is in the centre of goat circle ?
Maybe plotting the goat's position per second ?

I think it would also be informative to see the actual wolf prey boundary curve as an overlay as a point plot over the existing procedure simulation plot.

Within this wolf boundary curve, the prey can be caught, and outside it, it cannot.

@dharr 

Thank you, that confirms that the procedure code is working correctly.
Without animation, I don't really know how long the goat spins around.
There is a time calculation when the goat is caught
There is a starting angle , but the goat can start in two directions>
Try to get his in th e code too.

That manual code is a good approach.

Actually, there are only three possible positions for the wolf: outside the circle, inside the circle, and on the circle.
This can easily be calculated manually, so is there really a need for a procedure?

Note: Now the question arises: which direction would the goat have instinctively chosen?
FastPursuit2(1, 1, 1, 0, 5, 0.5, 5, 0.05, direction = "clockwise");
FastPursuit2(1, 1, 1, 0, 5, 0.5, 5, 0.05, direction = "counterclockwise");

After 5 seconds hunting on the goat by the wolf..

For 5 seconds hunting on the goat by the wolf : choosen clockwise by goat , but  in the end not.

achtervolgings_kromme_wolf_en_geit_mprimes_DEF1_15-9-2025.mw

@sand15 
You must use PMF ?
for PMF (Probability Mass Function) → Voor discrete variabelen

I  looked again to the code ,this is clockwise and  FastPursuit2(1, 1, 1, 0, 5, 0.5, 50, 0.05, direction = "counterclockwise") is also possible 
achtervolgings_kromme_wolf_en_geit_mprimes_DEF_14-9-2025_(2).mw
Strange curve from the wolf to  go to the goat ?

Improved FastPursuit2 procedure

FastPursuit2(5, 1.5, 1.0, 0, 2.0, 0., 1200, 0.05) example: the wolf is running in a almost concentric circle at almost fixed distant (not this plot)

achtervolgings_kromme_wolf_en_geit_mprimes_DEF_14-9-2025_.mw

achtervolgings_kromme_wolf_en_geit_mprimes_14-9-2025_.mw

Making now a FastPursuit2  procedure using dsolve :
sol := dsolve(sys union ics, {xw(t), yw(t)}, numeric, method = rkf45)

@Alfred_F 
 

Starting position and speed are decisive?

The goat continues to move in a circle

The wolf remains focused on the goat

Was it not with a pursuit curve?

Bring back  the number of sliders ? 

@Alfred_F 
Yes, that is a proof by contradiction, looks like on the proof voor the irrationality of square root two number
aside:
The ancient Greeks were confronted with the existence of the square root of 2 and believe that it came as a shock to their world view at that time.

periodiciteit_cos_achtergronden_mprimes7-9-2025.mw

@vv 
In my opinion, this is a mathematical proof sketch and the correct details should be filled in.
Getting this expression for cos(2pi.n) seems to be straight forwards ?, but now further..?

@Carl Love 

@Alfred_F 
niet_periodieke_functie_-mprimes_6-9-2025.mw